RESEARCH

Even if as of 2016 no «standard model» of the origin of life has yet emerged, most currently accepted models state that life arose on Earth between 3800 and 4100 million years ago. These first forms of live where single-celled organisms.

For most of the history of life on Earth there were only single-celled organisms. However, now there are many different fungi, algae, plants and animals that are multicellular organism (they are formed by aggregations of cells working together). Thus, even if we know that these single-celled organism eventually formed multicellular organisms (around 1500 millions of years ago), the origins of multicellarity are one of the most interesting topics in biology because we still do not know the way multicellarity arises.

A particular situation where cells form a cluster, in a process known as cell aggregation, arises when the motion of the cells is driven by a chemical gradient, i.e. the cells attempt to move towards higher (or lower) concentration of some chemical substance. This process is usually called chemotaxis. Then, multicellular aggregates and eventually tissue-like assemblies are formed when individual cells attach to each other as a consequence of the chemotactic movement and when this aggregation leads to subsequent cellular differentiation. That is, for instance, the case of the slime mold Dictyostelium Discoideum and bacterial populations, such as of Escherichia coli and Salmonella typhimurium.

A preliminary step towards a better understanding of chemotaxis and cell aggregation, was given by Keller and Segel with their 1970’s classical papers (see also the prior work by Patlak in the 1950’s). In these papers, Keller and Segel proposed a PDE system as a model of cell aggregation as a consequence of chemotactic movement. Then, mathematically, the appearance of cell aggregation is translated to the formation of a finite time singularity.

Part of our research focuses on whether the solution exists globally in time (i.e. no aggregation occurs).